## Mathematical Physics   ## Physics Mathematical Approximations

Authors: Harry A Watson

There are many ad hoc expressions for the mass ratio of the proton to the electron. the models presented here are different from others in that they rely strictly on volumes and areas. One geometry is based on ellipsoids constructed with values taken from one of the two number sets: {(4pi), (4pi-1/pi), (4pi-2/pi)} or {(4pi+2), (4pi-2), (4pi-2/pi)}. The product of the three values of each number set approximates the value given by CODATA for the mass ratio of the proton to the electron. Another approximate is formed from a solid ball of radius, r = (4pi-1/pi), with a conical sector, wedge, or internal ellipsoid removed. Each extracted solid has curved surface area of (4pi-1/pi)/(pi^2). With the advent of the Higg’s Boson, its value can be approximated by H^0 = (4pi)(4pi-1/pi)(4pi-2/pi)(4pi-3/pi)(4pi-4/pi). Define the function F as follows: Let the initial set be the positive integers, the final set be the real numbers, and the rule assigning each member of the initial set to one member of the final set: F(m) =(4pi)...(4pi-(m-1)/pi). Conclusion: The function F(2)=1836.15... approximates the experimental value of the mass ratio of the proton to the electron and F(4) approximates the mass ratio of the Higg's Boson to the electron. The neutron-to-electron ratio is approximated with ln(4pi)+F(2). Email: harry.watson@att.net